updates distributed service

README.md

@@ -20,3 +20,11 @@ _Warning: This project is not suitable for free Vercel plan. There is insufficie
 ### Deploying to Cloudflare Pages
 
 [![Deploy to Cloudflare Workers](https://deploy.workers.cloudflare.com/button?paid=true)](https://deploy.workers.cloudflare.com/?url=https://github.com/Trance-0/Notechondria)
+
+### Deploying as separated docker services
+
+Considering the memory usage for this project, it is better to deploy it as separated docker services.
+
+```bash
+docker-compose up -d -f docker/docker-compose.yaml
+```

content/Math4201/Math4201_L24.md

@@ -0,0 +1,110 @@
+# Math4201 Topology I (Lecture 24)
+
+## Connected and compact spaces
+
+### Connectedness
+
+Recall from example last lecture, there exists a connected space but not path-connected space.
+
+#### Lemma on connectedness
+
+Let $X$ be a topological space and $A\subseteq X$ is a connected subspace. If $B\subseteq X$ satisfies $A\subseteq B\subseteq \overline{A}$, then $B$ is connected. In particular, $\overline{A}$ is connected.
+
+<details>
+<summary>Proof</summary>
+
+Assume that $B$ is not connected. In particular, there are open subspaces $U$ and $V$ of $X$ such that $U\cap B, V\cap B$ is a separation of $B$.
+
+Take $U\cap A, V\cap A$, we show that this gives a separation of $A$.
+
+(i) Since $U,V$ are open, $U\cap A, V\cap A$ are open in $A$.
+
+(ii) Since $(U\cap B)\cap (V\cap B)=\emptyset$, $(U\cap A)\cap (V\cap A)=\emptyset$.
+
+(iii) Since $(U\cap B)\cup (V\cap B)=B$, any point in $B$ is in either $U\cap B$ or $V\cap B$.
+
+Since $A\subseteq B$, $(U\cap A)\cup (V\cap A)=A$.
+
+(iv) $U\cap A$ and $V\cap A$ is nonempty by assumption $U\cap B$ is nonempty and contains $x\in B\cap U\subseteq \overline{A}$. So any open neighborhood of $x$ have non-empty intersection $x'\in A$, so $x'\in U\cap A$ and $U\cap A$ is nonempty. Similarly, $V\cap A$ is nonempty.
+
+So $U\cap A$ and $V\cap A$ is a separation of $A$, which contradicts the assumption that $A$ is connected.
+
+Therefore, $B$ is connected.
+
+</details>
+
+#### Topologists' sine curve
+
+Let $A=\{(x,y)\in \mathbb{R}^2\mid y=\sin(1/x), x>0\}$. Then $A$ is connected, and also path-connected.
+
+$$
+\gamma(t) = (t, \sin(1/t)) \text{ for } t\in (0,1]
+$$
+
+However, take $\overline{A}=A\cup \{0\}\times [-1,1]$. Then $\overline{A}$ is not path-connected but connected.
+
+<details>
+<summary>Proof that topologists' sine curve is not path-connected</summary>
+
+We want to show $X=\overline{A}$ has no continuous path
+
+$$
+\gamma:([0,1])\to X
+$$
+
+such that $\gamma(0)=(0,0)$ and $\gamma(1)=(1,\sin(1))$.
+
+If there exists such a path, let $t_0\in [0,1]$ be defined as
+
+$$
+t_0=\sup\{t\in [0,1]\mid \gamma(t)=(0,x), x\in [0,1]\}
+$$
+
+By the assumption on $t_0$, we can find a sequence $\{t_n\}_{n\in\mathbb{N}_+}\subseteq A$ such that $t_n\to t$.
+
+By continuity of $\gamma$, we have $\gamma(t_n)\to \gamma(t_0)$, $(0,y_n)\to (0,y_0)$.
+
+Now focus on the restriction of $\gamma$ to $[t_0,1]$, $\gamma:[t_0,1]\to X$, $\gamma(t_0)=(0,y_0)$, $\gamma(1)=(1,\sin(1))$.
+
+$t\in (t_0,1]$, then $\gamma(t)\in$ graph of $y=\sin(1/x)$.
+
+Consider $\pi$ be the projection map to $x$-axis, $\pi\circ \gamma:[t_0,1]\to \mathbb{R}$, $\pi\circ \gamma(t_0)=0$ and $\pi\circ \gamma(1)=1$.
+
+In particular, there is a sequence $s_n\in [t_0,1]$ such that $s_n\to t_0$ and $\pi\circ \gamma(s_n)=\frac{1}{n\pi+\frac{\pi}{2}}$. (using intermediate value theorem)
+
+Then $\gamma(s_n)=(\frac{1}{n\pi},\sin(n\pi+\frac{\pi}{2}))=(\frac{1}{n\pi},(-1)^n)$.
+
+Since as $s_n\to t_0$, and $\gamma$ is continuous, then we get a contradiction that the sequence $\gamma(s_n)$ should converge to $(0,t_0)$ where it is not.
+
+</details>
+
+### Compactness
+
+Motivation: in real numbers.
+
+#### Extreme value theorem
+
+Let $f:[a,b]\to \mathbb{R}$ be continuous. Then there are $x_m,x_M\in [a,b]$ such that $f(x_m)\leq f(x)\leq f(x_M)$ for all $x\in [a,b]$.
+
+#### Definition of cover
+
+Let $X$ be a topological space. A covering of $X$ is a collection of subsets of $X$ that covers $X$.
+
+$$
+\{U_\alpha\}_{\alpha\in I}
+$$
+
+such that $X=\bigcup_{\alpha\in I} U_\alpha$.
+
+An open cover of $X$ is a covering of $X$ such that each $U_\alpha$ is open.
+
+#### Definition of compact space
+
+A topological space $X$ is compact if for any open covering $\{U_\alpha\}_{\alpha\in I}$ of $X$, there exists a finite subcovering $\{U_{\alpha_i}\}_{i=1}^n$ such that $X=\bigcup_{i=1}^n U_{\alpha_i}$.
+
+<details>
+<summary>Example of non-compact space</summary>
+
+Consider the interval $(0,1]$, the open covering $(\frac{1}{n},1]$ open in $(0,1]$, $\{(\frac{1}{n},1]\}_{n\in \mathbb{N}_+}$ has no finite subcovering.
+
+</details>

content/Math4201/_meta.js

@@ -27,4 +27,5 @@ export default {
     Math4201_L21: "Topology I (Lecture 21)",
     Math4201_L22: "Topology I (Lecture 22)",
     Math4201_L23: "Topology I (Lecture 23)",
+    Math4201_L24: "Topology I (Lecture 24)",
 }

content/_meta.js

@@ -1,4 +1,11 @@
 export default {
+  /**
+   * Do not remove the labels "Math Courses Start"
+   * and "Math Courses End" and "CSE Courses Start" and "CSE Courses End"
+   * or the separated builds will not work.
+   * 
+   * WE USE THESE LABELS TO BUILD THE SEPARATED WEBSITES FOR MATH AND CSE COURSES.
+   */
     menu: {
       title: 'Home',
       type: 'menu',
@@ -17,6 +24,7 @@ export default {
         }
       },
     },
+    /* Math Courses Start */
     Math3200: {
       type: 'page',
       theme:{
@@ -59,6 +67,8 @@ export default {
         timestamp: true,
       }
     },
+    /* Math Courses End */
+    /* CSE Courses Start */
     CSE332S: {
       title: 'CSE332S',
       type: 'page',
@@ -108,6 +118,7 @@ export default {
         timestamp: true,
       }
     },
+    /* CSE Courses End */
     Swap: {
       display: 'hidden',
       theme:{

docker/cse/Dockerfile

@@ -1,4 +1,4 @@
-# Dockerfile for CSE folders
+# Dockerfile for Math folders
 
 # Source: https://github.com/vercel/next.js/blob/canary/examples/with-docker-multi-env/docker/production/Dockerfile
 # syntax=docker.io/docker/dockerfile:1
@@ -28,10 +28,21 @@ FROM base AS builder
 WORKDIR /app
 COPY --from=deps /app/node_modules ./node_modules
 COPY . .
+RUN ls -la
 
-# 2.1 Remove unnecessary files for build with title not starting with CSE
-RUN find ./content -type d -not -name "CSE*" -exec rm -rf {} +
-RUN find ./public -type f -not -name "*.md" -exec rm -rf {} +
+# 2.1 Remove unnecessary files for build with title starting with CSE
+RUN cd ./content && find . -maxdepth 1 -type d -name "Math*" -exec rm -rf {} +
+RUN cd ./public && find . -maxdepth 1 -type d -name "Math*" -exec rm -rf {} +
+
+# 2.1.1 Check the updated folders
+RUN cd ./content && ls -la
+RUN cd ./public && ls -la
+
+# 2.2 Update the _meta.js files in the content folder
+RUN sed -i '/\/\* Math Courses Start \*\//,/\/\* Math Courses End \*\//d' ./content/_meta.js
+
+# 2.2.1 Check the updated _meta.js file
+RUN cat ./content/_meta.js
 
 # This will do the trick, use the corresponding env file for each environment.
 # COPY .env.production.sample .env.production
@@ -55,8 +66,8 @@ COPY --from=builder --chown=nextjs:nodejs /app/.next/static ./.next/static
 
 USER nextjs
 
-EXPOSE 3000
+EXPOSE 4201
 
-ENV PORT=3000
+ENV PORT=4201
 
 CMD HOSTNAME="0.0.0.0" node server.js

docker/cse/test-build.sh

@@ -0,0 +1 @@
+sudo docker build -t trance-0/notenextra-cse:v1.2.0 -f ./docker/cse/Dockerfile --no-cache --progress=plain .

docker/docker-compose.yaml

@@ -0,0 +1,30 @@
+services:
+  # you may need to update relative directories if you move this file
+  # default created directories is /docker/docker-compose.yaml
+  notenextra-math:
+    build:
+      context: ../
+      dockerfile: ./docker/math/Dockerfile
+      tags:
+        - trance0/notenextra-math:latest
+    restart: on-failure:5
+    ports:
+      - 13001:4201
+  notenextra-cse:
+    build:
+      context: ../
+      dockerfile: ./docker/cse/Dockerfile
+      tags:
+        - trance0/notenextra-cse:latest
+    restart: on-failure:5
+    ports:
+      - 13002:4202
+  nginx:
+    image: nginx:latest
+    ports:
+      - 13000:80
+    volumes:
+      - ./nginx.conf:/etc/nginx/nginx.conf
+    depends_on:
+      - notenextra-math
+      - notenextra-cse

docker/math/Dockerfile

@@ -28,12 +28,21 @@ FROM base AS builder
 WORKDIR /app
 COPY --from=deps /app/node_modules ./node_modules
 COPY . .
+RUN ls -la
 
 # 2.1 Remove unnecessary files for build with title starting with CSE
-RUN cd /app/content
-RUN find . -maxdepth 1 -type d -name "CSE*" -delete
-RUN cd /app/public
-RUN find . -maxdepth 1 -type d -name "CSE*" -delete
+RUN cd ./content && find . -maxdepth 1 -type d -name "CSE*" -exec rm -rf {} +
+RUN cd ./public && find . -maxdepth 1 -type d -name "CSE*" -exec rm -rf {} +
+
+# 2.1.1 Check the updated folders
+RUN cd ./content && ls -la
+RUN cd ./public && ls -la
+
+# 2.2 Update the _meta.js files in the content folder
+RUN sed -i '/\/\* CSE Courses Start \*\//,/\/\* CSE Courses End \*\//d' ./content/_meta.js
+
+# 2.2.1 Check the updated _meta.js file
+RUN cat ./content/_meta.js
 
 # This will do the trick, use the corresponding env file for each environment.
 # COPY .env.production.sample .env.production

docker/math/test-build.sh

@@ -0,0 +1 @@
+sudo docker build -t trance-0/notenextra-math:v1.2.0 -f ./docker/math/Dockerfile --no-cache --progress=plain .

docker/nginx.conf

@@ -0,0 +1,23 @@
+    # Example for conf.d/default.conf
+    server {
+        listen 80;
+        server_name localhost;
+
+        location /Math* {
+            proxy_pass http://notenextra-math:4201;
+            proxy_set_header Host $host;
+            proxy_set_header X-Real-IP $remote_addr;
+            proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+            proxy_set_header X-Forwarded-Proto $scheme;
+        }
+
+        location /CSE* {
+            proxy_pass http://notenextra-cse:4202;
+            proxy_set_header Host $host;
+            proxy_set_header X-Real-IP $remote_addr;
+            proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+            proxy_set_header X-Forwarded-Proto $scheme;
+        }
+
+
+    }

next-sitemap.config.js

@@ -1,8 +1,8 @@
 /** @type {import('next-sitemap').IConfig} */
-export default {
+module.exports = {
   siteUrl: 'https://notenextra.trance-0.com',
-    changefreq: 'weekly',
+  changefreq: 'daily',
   priority: '0.5',
   generateIndexSitemap: false,
   exclude: ['/icon.svg']
-  }
+}

next.config.mjs

@@ -26,8 +26,8 @@ export default bundleAnalyzer(withNextra({
   },
   experimental: {    
     webpackMemoryOptimizations: true,
-    staticGenerationMaxConcurrency: 2,   // try 1–3
-    staticGenerationMinPagesPerWorker: 1 // keep small
+    staticGenerationMaxConcurrency: 2,   // try 1–3, default is 8
+    staticGenerationMinPagesPerWorker: 1 // keep small, default is 25
   }
 }))